Algebraic equations of state for the liquid crystalline phase behavior of hard rods

Peters, Vincent F. D.; Vis, Mark; Wensink, H. H.; Tuinier, Remco

doi:10.1103/physreve.101.062707

Cited by 14 publications

(39 citation statements)

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“…In this model, the colloidal rods cannot penetrate each other and do not interact otherwise. Computer simulations , revealed that dispersions of hard spherocylinders can assume isotropic (I), nematic (N), smectic-A (SmA), AAA, and ABC phase states (see Figure for a sketch of these phase states). , The thermodynamically preferred phase state depends on the concentration and length–diameter aspect ratio. In both the isotropic and nematic phases, there is no positional order, but in the nematic phase, the rods assume a preferred orientation.…”

Section: Introductionmentioning

confidence: 99%

Multiphase Coexistences in Rod–Polymer Mixtures

et al. 2021

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Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod−polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer−rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod−polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. (J. Chem. Phys. 107, 1997 1551.

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Section: Introductionmentioning

confidence: 99%

Multiphase Coexistences in Rod–Polymer Mixtures

et al. 2021

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“…Using a Gaussian approximation for the distribution of rod angles with respect to the nematic director, one can construct algebraic equations of state [37]. Given that PL theory tends to be more accurate for weakly anisotropic rods while SPT has proven more reliable for long rods, we employ a straightforward sigmoidal interpolation procedure in order to accurately cover the full range of aspect ratios [40]. We emphasize that the observed phase behavior is robust and is not qualitatively affected by details of the rod-polymer model (see Fig.…”

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confidence: 99%

“…Phase behavior of hard spherocylinders as a function of rod volume fraction η and aspect ratio D=L from both theory (solid curves)[40] and simulation (data points)[14]. The stable phases include the isotropic (I), nematic (N), smectic A (SmA), AAA crystal, and ABC crystal phase.…”

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“…In the AAA phase the rods of adjacent layers are stacked on top of each other, while in the ABC phase they are stacked in between the rods of adjacent layers. For all these three phases we have used an extended cell theory similar to Graf and Löwen [38] and the results were subsequently cast into algebraic equations [40]. For the SmA phase this includes a thermodynamic description of 2D disks that captures the inplane fluidity of rods projected onto the smectic plane.…”

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Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures

Peters¹,

Vis²,

García³

et al. 2020

Phys. Rev. Lett.

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Using a minimal algebraic model for the thermodynamics of binary rod-polymer mixtures, we provide evidence for a quintuple phase equilibrium; an observation that seems to be at odds with the Gibbs phase rule for two-component systems. Our model is based on equations of state for the relevant liquid crystal phases that are in quantitative agreement with computer simulations. We argue that the appearance of a quintuple equilibrium, involving an isotropic fluid, a nematic and smectic liquid crystal, and two solid phases, can be reconciled with a generalized Gibbs phase rule in which the two intrinsic length scales of the athermal colloid-polymer mixture act as additional field variables.

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“…where Λ is the De Broglie wavelength. For the range of reservoir concentrations used in this work it is expected that the rod-like particles do not form a nematic phase but behave as a fluid 22,43 . Therefore, the scaled particle theory (SPT) result for a fluid dispersion of hard spherocylinders 44 is used for the osmotic pressure in the reservoir:…”

Section: A Semi-grand Potentialmentioning

confidence: 99%

Phase stability of colloidal mixtures of spheres and rods

Opdam

Guu

Schelling

et al. 2021

The Journal of Chemical Physics

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We determined the phase boundaries of aqueous mixtures containing colloidal rod-like fd-viruses and polystyrene spheres using diffusing-wave spectroscopy and compared the results with free volume theory predictions. Excluded volume interactions in mixtures of colloidal rods and spheres lead to mediated depletion interactions. The strength and range of this attractive interaction depend on the concentrations of the particles, the length L and diameter D of the rods and the radius R of the spheres. At strong enough attraction, this depletion interaction leads to phase separation. We experimentally determined the rod and sphere concentrations where these phase transitions occur by systematically varying the size ratios L/R and D/R and the aspect ratio L/D. This was done by using spheres with different radii and modifying the effective diameter of the rods through either the ionic strength of the buffer or anchoring a polymeric brush to the surface of the rods. The observed phase transitions were from a binary fluid to a colloidal gas/liquid phase coexistence which occurred already at very low concentrations due to the depletion efficiency of highly anisotropic rods. The experimentally measured phase transitions were compared to phase boundaries obtained using free volume theory (FVT), a well established theory for calculating the phase behaviour of colloidal particles mixed with depletants. We find good correspondence between the experimental phase transitions and the theoretical FVT model where the excluded volume of the rod-like depletants was explicitly accounted for in both the reservoir and the system.

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Algebraic equations of state for the liquid crystalline phase behavior of hard rods

Cited by 14 publications

References 50 publications

Multiphase Coexistences in Rod–Polymer Mixtures

Multiphase Coexistences in Rod–Polymer Mixtures

Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures

Phase stability of colloidal mixtures of spheres and rods

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